In the end, the scientists divided their volunteers into four groups, based on their e4 status and exercise habits. One group included those people with the e4 gene who did not exercise; another consisted of those with the e4 gene who did exercise; and the other two groups were composed of those without the gene who did or did not regularly exercise.

The scientists then scanned their volunteers’ brains, with particular emphasis on their hippocampi. Eighteen months later, they repeated the scans.

The members of the group carrying the e4 gene who did not exercise had undergone significant atrophy of their hippocampus. It had shrunk by about 3 per cent, on average.

Those volunteers who carried the e4 gene but who regularly exercised, however, showed almost no shrinkage of their hippocampus. Likewise, both groups of volunteers who did not carry the e4 gene showed little change to their hippocampus.

In effect, the brains of physically active volunteers at high risk for Alzheimer’s disease looked just like the brains of people at much lower risk for the disease, said Stephen M Rao, a professor at the Schey Center for Cognitive Neuroimaging at the Cleveland Clinic, who oversaw the study. Exercise appeared to have been protective.

Meanwhile, the brains of sedentary people at high risk appeared to be slipping, structurally, toward dysfunction. “This occurred in a very compressed time frame,” said Dr Rao, who described the differences in brain structure as “quite significant”.